1) Pick a number from 0 to 9 for the first digit. If the number is 0 the process terminates with the number 0.
2) Pick another number from 0 to 9. If it is greater than the previous number, append it to the previous to create a number with one more digit. If not then terminate the process.
3) Repeat step 2 until the process terminates.

The resulting number will be n digits long and have strictly increasing digits where n is an integer from 0 to 9.

Find the probability distribution for n.

Notes: Numbers are chosen with a uniform random probability.
0 is considered a 0 digit number.
This is an extension of Evaluate probabilities.